4-01 - 4-1. Determine the mass density, , for the mixing...

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4-1. Determine the mass density, ρ , for the mixing process illustrated in Figure 4-1. 4-1. The mixing process illustrated in Figure 4-1 is a batch process in which the mass of each species is conserved. We express this idea as ooo ,, A AA B BB C C VVVVV ρ= ρ ρ= ρ ρ= ρ C V o 3 (1) and we can solve for the three species densities in the final mixture to obtain (2) oo /, /, / AA A BB B CC C VV VV VV ρ= ρ ρ= ρ ρ= ρ The numerical results are given by (3) 33 0.283 g/cm , 0.317 g/cm , 0.356 g/cm ABC ρ= ρ= ρ= This type of calculation is intuitively obvious; however, it is worthwhile to understand the framework of the calculation in terms of the concepts presented in Chapter 4. The macroscopic mass balance for species A can be expressed as () () () () AA A tt t d dV dA r dV dt ρ+ρ− ⋅ = ∫∫ vw n VA V A (4) where V represents a control volume that properly represents the mixing process during which species B and C are added to species A . Since there is no chemical reaction involving species A , and since no species A enters or leaves the system at the control surface, A , Eq. 4 takes the form () t ( ) t () 0 A t d dV dt ρ= V (5) Integration from the initial time, when all three species are in separate containers, to the final time when all three species are mixed, lead to (6) 12 o () ( ) A tt dV dV ρ=ρ ∫∫ VV A 2 Since the species density is uniform, this result simplifies to
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This note was uploaded on 07/15/2010 for the course ECM 051 taught by Professor B.g.higgins during the Winter '10 term at UC Davis.

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4-01 - 4-1. Determine the mass density, , for the mixing...

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